Journal of Applied Mathematics & Bioinformatics

Improved Approximate Solutions for Nonlinear Evolutions Equations in Mathematical Physics Using the Reduced Differential Transform Method

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• Abstract

  In this paper, an improved method called the Reduced Differential Transform Method (RDTM) was used to obtain approximate numerical and exact solutions for three different types of nonlinear partial differential equations (NLPDEs), such as; Gardner equation, Variant Nonlinear Water Wave equation (VNWW), and the Fifth-Order Korteweg-de Vries (FKdV) equation. The theoretical analyses of the RDTM are investigated for these equations and are calculated in the form of a series with easily computable terms. The results we obtained are compared with the analytical solutions obtained by other methods used in the past. One can conclude that only few terms of the series expansion are required to obtain approximate solutions using the RDTM with an excellent accuracy. Most of the symbolic and numerical computations were performed using Mathematica software.